Talk about a life-changing moment. Naomi Watts is recalling the time she nearly drowned. She was 14, travelling with her mother and older brother Ben. "We were emigrating to Australia," she says, "and we stopped off in Bali."

Leaving the England where she had grown up, it was supposed to be the beginning of a new life for Watts and her family but it almost ended in tragedy. At the beach, she and her mother were in the sea when they got caught in a riptide. "I wasn't a very good swimmer at that point. I'd been living in England and not spending much time at the beach!"

Even now, the petite 44-year-old is fragile-looking, a mix of the articulate and the anxious; it's hard to imagine her teenage self battling Mother Nature. "We got caught in a rip, and I just got very, very tired. Now I know how to deal with a rip – you don't try to swim to the shore, you just let yourself go with the tide. But my instincts were telling me otherwise. I remember getting scared by it and my mum was very scared." Her breathing is a little heavy now, the memory of the event – some three decades ago – still all-too-fresh. "I'm still scared of swimming in waves."

It seems almost apt that Watts should have endured a near-death experience so young, given how she's become an actress synonymous with the sombre. Think of her real-life CIA operative Valerie Plame whose identity is exposed in Fair Game. Or her mother in Michael Haneke's US remake of his own home-invasion story Funny Games, tortured and tormented by two attackers. In 21 Grams, for which she received an Oscar nomination, she was a recovering drug addict who returns to her former ways after her husband and children are killed in a road accident. Even when she does comedy – such as Woody Allen's You Will Meet a Tall Dark Stranger – she plays neurotic.

Today, she greets me with a nervy smile, a nervousness pertinent to the disquieting subject matter of her latest film, The Impossible, a harrowing movie set around the Boxing Day tsunami of 2004, which devastated lives across coastal regions of South-east Asia. Watts plays Maria, a mother of three boys who gets separated from her two youngest and her British businessman husband (Ewan McGregor) when the wave hits, sustaining horrific injuries. Earlier this month, she won Best Actress nominations for the role at the Golden Globe and Screen Actors Guild Awards, both traditional early indicators of Oscar voting.

Set in the Thai beach resort of Khao Lak, the film is based on the real-life experiences of Spanish family the Balons, and was partly shot in the very hotel, The Orchid, where they were holidaying when the wave struck. "You could still see the wreckage in certain places," Watts says. "The hotel was completely back to normal, but here and there you would see things, reminders. The wetland, the marsh had completely changed – the way the trees were growing or not. Like any massive disaster, people are still trying to process it. The need to talk about it never goes away, no matter how many years on you are from it."

Watts' performance is an instinctual blend of sheer terror and wilful determination as she tries desperately to locate her family amid the chaos. "She's very real," notes McGregor, who previously worked with the actress on the psychological thriller Stay. "If you think about her character – she's a mother, a wife, with worries about her future and thoughts about where they should live. Then for the rest of the movie, she's injured, scared, frightened to leave her kids, thinks she might die. And in the hands of a lesser actress, it would be very easy for that to be a one-note performance. But she really adds so much colour and so much depth. It was a feat of great acting."

Understandably, making The Impossible brought all Watts' fears of the water flooding back. For the film's nerve-shredding 10-minute recreation of the tsunami, Watts spent more than a month in a giant water tank in a studio in Alicante, being buffeted around like a cork in a whirlpool. "A lot of it wasn't acting, because you're literally being sucked under, and I was genuinely gasping for air," she says, recalling one particularly traumatic moment. Under water, she was locked into a contraption, feet tied in, which spun her round – then inadvertently changed direction. "I couldn't get out, and I thought, 'Oh God, they can't stop it!'"

Those swift intakes of breath have started again. "I remember getting quite upset because I thought, 'Maybe they were trying a trick to make me look more scared.'" But, however it sounds, Watts is no drama queen, clamouring for attention. "You cannot complain because think about what these people went through," she says, simply. Now a mother of two, it's the sort of film that makes you want to hug your kids tighter, she says. "Knowing the story is real and that the people who were close to it are still suffering, wanting to connect with your family is…" She trails off, leaving the word 'inevitable' hanging.

Watts, who has been with the actor Liev Schreiber since they met on the 2006 film The Painted Veil, had their two boys – Sasha, five, and Sammy, four – with her for the Thailand leg of the shoot. Perhaps not surprisingly, she found it impossible to explain The Impossible to them: "They're prone to nightmares if you introduce big scary topics. Being a mum, it's your duty to leave [the character] there on the set. That never used to be the case, but now that's my life, and the minute I open that door, I'm done… and I'm there with my kids."

Even before her own Bali nightmare, Watts learnt the value of life at a young age. Born in Shoreham, Kent, she saw her mother Myfanwy, a Welsh-born antiques dealer and amateur actress, separate from her father, Peter Watts, when she was just four. A sound engineer for Pink Floyd, Watts will be known by fans for his manic laughter that can be heard across the band's seminal Dark Side of the Moon album. But by the time his daughter had turned seven, he had died, aged 30, from a suspected drugs overdose. "There was a lot of sadness in my life when I was a child," she says. "Mum had to struggle a lot to bring us up and I have enormous admiration for her."

In the wake of her father's death, she and her mother and brother were forever moving around the UK – at one point living with her grandparents in Wales. Then Myfanwy decided to relocate to Australia, heading – via that almost fateful layover in Bali – to Sydney. It's not hard to imagine the fair-skinned, frail Watts feeling isolated, a stranger in a strange land. "It took time to feel like I fitted in," she nods. "To Australian people, I'm English, and to the English, I'm Australian." It was not long before this teenaged outsider gravitated towards acting, inspired as she had been ever since seeing her mother on stage as Eliza Doolittle in an amateur production of My Fair Lady when she was five.

Signing up for acting classes, Watts became determined to make it her career. It was at this point, at high school, that she met Nicole Kidman; the two became firm friends, even starring together in 1991's Flirting, one of Watts' earliest films. But then Kidman met and married Tom Cruise, and travelled on a fast-track to stardom. As her friend soared, Watts was left behind, dealing with that endless round of auditions, callbacks, knockbacks and disappointments that most actors face. Even when she got a gig – in the 1995 big-screen comic-book movie Tank Girl, say – it fell flat, the film flopping notoriously.

Moving to LA, even acting as Kidman and Cruise's nanny for a time, it got no better for Watts. "There were so often times when I thought about throwing in the towel, feeling very frustrated. There's so much competition and it's so hard to shine when you're being told who you are – too young, too old, too serious, too funny. Whatever. Basically, you start believing it, and lose confidence in yourself. The reason we're actors is that we don't have the strongest identities anyway. We love to attach ourselves to other identities. But I really felt like I was losing a sense of who I was. I was un-hireable."

Then along came David Lynch and Mulholland Drive. Cast, ironically enough, as a wide-eyed starlet dreaming of a glittering Hollywood career, Watts shot a pilot with Lynch for what was intended to be a TV series in the mould of his own Twin Peaks. Three networks turned it down, leaving Watts heartbroken. But then came the turning point: Lynch found funding to shoot more footage and turn the pilot into a feature film. Immediately heralded for her performance, Watts didn't look back, working with such industry giants as David Cronenberg (Eastern Promises), Peter Jackson (King Kong) and Clint Eastwood (J Edgar).

It was around this time that she met Schreiber, having come out of relationships with director Stephen Hopkins (Lost in Space) and the late Heath Ledger (with whom she worked on outlaw tale Ned Kelly). While they have yet to marry – Schreiber claims he has given her a ring – they're the antithesis of the Hollywood glamour couple. Though they're based in New York, you won't see them at parties or premieres, unless they're supporting each other. Watts, who calls Schreiber "a very hands-on dad", will work only when he's free and vice versa.

A sensitive, soulful stage actor with movie credits including Salt, Defiance and The Manchurian Candidate, Schreiber was also a child of divorce who grew up with his mother, living as squatters in abandoned buildings. He was forbidden even to watch colour movies. "We both had, in different ways, difficult childhoods. And painful, sad ones," he told me recently. "I think we, if anything, could be accused of spoiling our children wildly. But we're also very paranoid about how profound an effect you can have on your children if you're not careful."

While Watts did take time off around the time of her pregnancies, it barely feels as if she's stopped working in the decade since Mulholland Drive. "It is hard to wrap your head around," she admits. "Just recently I felt like, 'Oh, God, what if it stops soon?' And I guess that's human nature, particularly for women in our industry – there is a fear and a rule that it's supposed to stop. Although I feel like I'm getting good calls still. I feel very, very lucky. And the roles are, in a way, more interesting. The longer the life, the fuller it is, and the roles should reflect that."

In some ways, it helps that Watts' career only took off in her thirties. We never saw her in that ingénue phase (unless you were watching her briefly in Aussie soap Home and Away). "I think the best thing about it is that I had a better sense of myself. I've always thought of myself as a late bloomer, and probably I might have been too impressionable if I'd got into it earlier, and I might have made bad choices or been seduced into doing some 'big thing'. I know what I like, I know what speaks to me. I'll do it because I want to, not because someone told me I should."

For all that, Watts is not afraid of the iconic. King Kong saw her take on the Fay Wray role, the ultimate damsel; she was, at one point, set to play Marilyn Monroe in Blonde, an adaptation of Joyce Carol Oates' book; a remake of Hitchcock's The Birds was mooted; and there's talk that she will play explorer/archaeologist Gertrude Bell in the forthcoming project Queen of the Desert. But all of that pales against her next role, as the lead in Diana, which traces the Princess of Wales' relationship with Pakistani heart surgeon Hasnat Khan in the lead-up to her death in 1997.

The prospect of playing the People's Princess is "very scary", she says. "If you're not scared by it, it's probably not worth doing, is it?" The film is directed by Oliver Hirschbiegel, who made Downfall about the last days of Hitler – "an absolute masterpiece of a film", says Watts. This is different, however. "It really concentrates on the last few years of her life. Obviously a tragic ending. But fascinating." Her preparation included six weeks of vocal training with a dialogue coach and repeated viewings of Martin Bashir's famous 1995 interview.

Early shots – with Watts wearing replica dresses, a (very subtle) prosthetic nose and wig – are quite eerie. She admits her main concern is for Diana's sons, Prince William and Prince Harry. "We're trying to show her in the best possible light as a human being, full of different layers," she says.

If that weren't enough to turn 2013 into a major year for Watts, she's also to be seen in Movie 43, a rare chance to flex her funny bone in an all-star ensemble comedy, featuring Hugh Jackman, Kate Winslet and a host of others in a series of X-rated sketches. She also has Sunlight Jr, the story of a couple dealing with an unexpected pregnancy, co-starring Matt Dillon; and Two Mothers, a take on Doris Lessing's novel about best friends who fall for each other's sons.

"Talk about rich, controversial material," she smiles. "It was very challenging. The 'boys' were young. Too young! The guy I play opposite was 19!" Like Diana, it's yet another gutsy role that so many actresses would shy away from. But then Watts isn't like most pampered starlets. "If you put vanity before any film, you're doomed," she shrugs. "Sometimes you get to look great, like a movie star, and sometimes you don't."

'The Impossible' (12A) opens on 1 January. 'Movie 43' (15) is released on 25 January